write a quadratic function in vertex form. write the equation for the axis of symmetry of the parabola.

Missing data.

To write a quadratic function in vertex form, we need the equation in the form of:

f(x) = a(x - h)^2 + k

where (h, k) represents the coordinates of the vertex of the parabola.

Now, to find the vertex coordinates (h, k) and the equation for the axis of symmetry, we'll need more information. Either the quadratic function itself or some additional points on the parabola's graph are required.

If we have the quadratic function in standard form, which is ax^2 + bx + c = 0, we can use a concept called "completing the square" to convert it to vertex form.

Here's the step-by-step process:

1. Start with the equation in standard form: f(x) = ax^2 + bx + c.

2. Complete the square for the x terms by adding and subtracting (b/2a)^2 inside the parentheses:
f(x) = a(x^2 + (b/a)x) + c.

3. Rewrite the equation by factoring out a from the first two terms:
f(x) = a(x^2 + (b/a)x + (b/2a)^2 - (b/2a)^2) + c.

4. Simplify the expression inside the parentheses by applying the perfect square binomial formula:
f(x) = a(x + (b/2a))^2 + c - (b^2/4a).

Now the equation is in vertex form: f(x) = a(x - h)^2 + k, where h = -b/2a (-b divided by 2a) and k = c - (b^2/4a) (c minus b squared divided by 4a).

The equation for the axis of symmetry, which represents the vertical line of symmetry of the parabola, is given by x = h. Hence, the equation for the axis of symmetry is x = -b/2a.

Remember to substitute specific values of a, b, and c to match the given quadratic function to write the complete equations.